Non-Existence of Stabilizing Policies for the Critical Push-Pull Network and Generalizations

The push-pull queueing network is a simple example in which servers either serve jobs or generate new arrivals. It was previously conjectured that there is no policy that makes the network positive recurrent (stable) in the critical case. We settle this conjecture and devise a general sufficient condition for non-stabilizability of queueing networks which is based on a linear martingale and further applies to generalizations of the push-pull network.Comment: 14 pages, 3 figure

Stability and performance for multi-class queueing networks with infinite virtual queues

We generalize the standard multi-class queueing network model by allowing both standard queues and in??nite virtual queues which have infinite supply of work. We pose the general problem of finding policies which allow some of the nodes of the network to work with full utilization, and yet keep all the standard queues in the system stable. Towards this end we show that re-entrant lines, systems of two re-entrant lines through two service stations, and rings of service stations can be stabilized with priority policies under certain parameter restrictions. We further establish simple diffusion limits for the departure and work allocation processes. The analysis throughout the paper depends on model and policy and illustrates the difficulty in solving the general problem

Diffusion parameters of flows in stable queueing networks

We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes the system stable. An example is a generalized Jackson network with load less than unity and any work conserving policy. We find a simple diffusion limit for the inter-queue flows with an explicit computable expression for the covariance matrix. Specifically, we present a simple computable expression for the asymptotic variance of arrivals (or departures) of each of the individual queues and each of the flows in the network

Markov chains with discontinuous drifts have differential inclusions limits. Application to stochastic stability and mean field approximation.

In this paper, we study deterministic limits of Markov processes having discontinuous drifts. While most results assume that the limiting dynamics is continuous, we show that these conditions are not necessary to prove convergence to a deterministic system. More precisely, we show that under mild assumptions, the stochastic system is a stochastic approximation algorithm with constant step size that converges to a differential inclusion. This differential inclusion is obtained by convexifying the rescaled drift of the Markov chain. This generic convergence result is used to compute stability conditions of stochastic systems, via their fluid limits. It is also used to analyze systems where discontinuous dynamics arise naturally, such as queueing systems with boundary conditions or with threshold control policies, via mean field approximations.Ce document étudie des limites d'échelle de chaînes de Markov ayant une dérive discontinue. Alors que beaucoup de travaux sur le sujet supposent que la dérive est continue, nous montrons que cette condition n'est pas nécessaire pour obtenir une limite déterministe. Nous montrons que sous des hypothèses faibles, un passage à l'échelle d'une chaîne de Markov peut être vu comme un algorithme d'approximation stochastique à pas constant, qui converge vers l'ensemble des solutions d'une inclusion différentielle. Cette inclusion est obtenue à partir d'une convexification de la dérive du processus initial. Cette méthode est générique et permet de calculer la région de stabilité de nombreux systèmes stochastique, en étudiant leur limite fluide. Elle permet aussi d'étendre les techniques d'approximation champ moyen à des systèmes où les discontinuités apparaissent naturellement, comme des réseaux de files d'attente ou des systèmes contrôlés par une politique à seuil

Journal of Telecommunications and Information Technology, 2018, nr 1

kwartalni

Understanding Customer Switching Behaviour in the Retail Banking Sector: The Case of Nigeria and the Gambia

This thesis examines customer switching behaviour in Nigeria and Gambia, focusing on the retail banking sector. The study’s key objective is to provide new knowledge on customer banking behaviour in the retail banking sector. The study is grounded in Bansal et al.’s (2005) push-pull-mooring model. A qualitative method was employed in the data collection, incorporating a triangulation approach, whereby direct observations were combined with thematic interviews and focus group discussions. The intention behind this method was to increase the validity of the research results. Ultimately, the study findings indicate significant factors and subfactors influencing customer switching behaviour in the retail banking sector. The results are categorised as push, pull, or mooring factors. It identifies seven push factors with thirteen subfactors, four pull factors with ten subfactors, and six mooring factors with three subfactors. The study’s significant contribution to existing knowledge of services marketing is the identification of new and emerging constructs, thus extending the existing knowledge in the literature. The study’s findings support numerous results of prior relevant research, while some findings disagree with those of previous research. Furthermore, the new constructs that emerge from this research are highly relevant to today’s consumers. For example, factors like banking products, perceived knowledge of banking products, perceived relative security of banking products, satisfaction with the current bank, emotions (e.g., regret or anger), liquidity challenges, bank staff career development prospects, and ethical banking issues are the study’s unique contributions to the push factors and subfactors. In addition, the emerging pull factors and subfactors include technological advancement, coronavirus pandemic-induced switching, a bank’s physical appearance, positive banking expectations, a bank’s relative proximity, expected switching benefits, perceived usefulness of a bank’s digital platforms, perceived ease of banking transactions, personalised banking offerings, and repositioning banking business models. Lastly, the new mooring factors and subfactors identified in this study are inertia, changes in customer needs or tastes, involuntary switching, and bank responsiveness. Consequently, the author has developed a framework/model based on the findings of this study. The new framework/model presented comprehensive results with practical implications and a valuable contribution to the current knowledge of customer switching behaviour

Space Communications: Theory and Applications. Volume 3: Information Processing and Advanced Techniques. A Bibliography, 1958 - 1963

Annotated bibliography on information processing and advanced communication techniques - theory and applications of space communication

Positive Harris recurrence and diffusion scale analysis of a push pull queueing network

We consider a push pull queueing network with two servers and two types of job which are processed by the two servers in opposite order, with stochastic generally distributed processing times. This push pull network was introduced by Kopzon and Weiss, who assumed exponential processing times. It is similar to the Kumar–Seidman Rybko–Stolyar (KSRS) multi-class queueing network, with the distinction that instead of random arrivals, there is an infinite supply of jobs of both types. Unlike the KSRS network, we can find policies under which our push pull network works at full utilization, with both servers busy at all times, and without being congested. We perform fluid and diffusion scale analysis of this network under such policies, to show fluid stability, positive Harris recurrence, and to obtain a diffusion limit for the network. On the diffusion scale the network is empty, and the departures of the two types of job are highly negatively correlated Brownian motions. Using similar methods we also derive a diffusion limit of a re-entrant line with an infinite supply of work